1. Field of the Invention
This invention relates to adaptive windowing of Fast Fourier Transform (FFT) data to reduce spectral leakage and increase sidelobe rejection. More specifically, the present invention is directed to methods using multiple cosine window structures with 5- and 7-point convolution formulas to extend shift-variant data adaptive windows used in spatial variant apodization digital image processing applications.
2. Discussion of the Related Art
Fast Fourier Transforms (FFTs) are used for processing observed signals. Weighing functions, referred to as windows, are applied to the data to reduce the spectral leakage associated with finite observation intervals. Thus, in applying windows to a sample data harmonic analysis, undesirable effects due to spectral leakage are attempted to be removed. An indicator of how well a window suppresses leakage is the peak sidelobe level. Another indicator is the asymptotic rate of fall off of the sidelobes. However, an undesirable property associated with windowing is that the main lobe is widened. This results in a loss of spectral resolution.
To reduce spectral leakage, typical FFT based spectral analysis usually incorporates pre-transform windowing. Standard windows taper the finite length records of data at the edges, thus reducing sidelobe interference. However, because typical FFT based processing of time series data usually includes a time-domain windowing operation, leakage due to discontinuities of the data at the edges of the finite records tend to mask significant components of the signal. This is because the Discrete-Fourier Transform periodically extends the finite data records. In standard windowing techniques, the finite record is multiplied by a time-domain window that tapers the data to zero on the edges. The tapering of the data at the edges has the effect of spectrally reducing the sidelobes of the window. Associated with this windowing is the undesirable property that the mainlobe is widened. This results in a loss of spectral resolution.
It is necessary that a technique be developed to increase spectral resolution and sidelobe rejection.